191° Вправа 191Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 57

191. Піднесіть до степеня.

Підносимо до степеня і чисельник, і знаменник: ${\displaystyle {\left(\frac{A}{B}\right)}^n=}$${\displaystyle \frac{A^n}{B^n}}$; ${\displaystyle {\left(a^m\right)}^n=}$${\displaystyle a^{mn}}$.

1) ${\displaystyle {\left(\frac{a^3}{4}\right)}^2=}$${\displaystyle \frac{{\left(a^3\right)}^2}{4^2}=}$${\displaystyle \frac{a^6}{16}}$;

2) ${\displaystyle {\left(\frac{7}{c^2}\right)}^3=}$${\displaystyle \frac{7^3}{{\left(c^2\right)}^3}=}$${\displaystyle \frac{343}{c^6}}$;

3) ${\displaystyle {(-\frac{5a}{b^3})}^2=}$${\displaystyle \frac{5^2{a}^2}{{\left(b^3\right)}^2}=}$${\displaystyle \frac{25a^2}{b^6}}$;

4) ${\displaystyle {(-\frac{3a^6}{b^3})}^3=}$${\displaystyle -\frac{3^3{\left(a^6\right)}^3}{{\left(b^3\right)}^3}=}$${\displaystyle -\frac{27a^{18}}{b^9}}$.